a car salesperson is paid a base salary of $1800 per month even if she does not sell any cars. she is also…

a car salesperson is paid a base salary of $1800 per month even if she does not sell any cars. she is also paid an additional set amount of money for each car she sells. last month, the salesperson sold 8 cars. her total salary for the month was $2600.\ndefine a unit for the salespersons monthly earnings. enter a variable for the number of cars sold and use this variable to write an expression for the salespersons monthly earnings.\n1. how much would she make in one month if she sold eighteen cars?\n2. if she made $3200 in one month, how many cars did she sell?

a car salesperson is paid a base salary of $1800 per month even if she does not sell any cars. she is also paid an additional set amount of money for each car she sells. last month, the salesperson sold 8 cars. her total salary for the month was $2600.\ndefine a unit for the salespersons monthly earnings. enter a variable for the number of cars sold and use this variable to write an expression for the salespersons monthly earnings.\n1. how much would she make in one month if she sold eighteen cars?\n2. if she made $3200 in one month, how many cars did she sell?

Answer

Explanation:

Step1: Find the amount per car sold

Let $x$ be the number of cars sold and $y$ be the monthly earnings. The base - salary is $1800$. When $x = 8$, $y=2600$. The additional amount earned from selling 8 cars is $2600 - 1800=800$. So the amount per car sold (slope $m$) is $\frac{2600 - 1800}{8}=\frac{800}{8}=100$ dollars per car.

Step2: Write the linear - equation for monthly earnings

The linear equation for the monthly earnings is $y=100x + 1800$, where 1800 is the y - intercept (the base salary).

Step3: Solve for the first question

If $x = 18$, then $y=100\times18+1800$. $y = 1800+1800=3600$.

Step4: Solve for the second question

If $y = 3200$, then $3200=100x + 1800$. Subtract 1800 from both sides: $3200−1800 = 100x$, so $1400 = 100x$. Divide both sides by 100: $x=\frac{1400}{100}=14$.

Answer:

  1. $3600$
  2. $14$